lab5
Joshua Wiseman
2023-02-12
Rar
Among Us Drip. I thought it was funny, idk.
Task 1
Working Directory
getwd()## [1] "/home/joshua/Desktop/MainFolder/OuClasses/Spring 2023/Applied Statistical Methods/FALL224753wise0046/LABS/LAB5"Task 2
mybin function
mybin=function(iter=100,n=10, p=0.5){
# make a matrix to hold the samples initially filled with NA's
sam.mat=matrix(NA,nrow=n,ncol=iter, byrow=TRUE)
#Make a vector to hold the number of successes in each trial
succ=c()
for(i in 1:iter){
#Fill each column with a new sample
sam.mat[,i]=sample(c(1,0),n,replace=TRUE, prob=c(p,1-p))
#Calculate a statistic from the sample (this case it is the sum)
succ[i]=sum(sam.mat[,i])
}
#Make a table of successes
succ.tab=table(factor(succ,levels=0:n))
#Make a barplot of the proportions
iter.lab = paste0("iter = ", iter)
n.lab = paste0("n = ",n)
p.lab = paste0("p = ",p)
lab = paste0(iter.lab, n.lab, p.lab, sep=", ")
barplot(succ.tab/(iter), col=rainbow(n+1), main="Binomial simulation", xlab="Number of successes")
succ.tab/iter
}100 iterations Plot
bin100 = mybin(iter = 100, n = 10, p = 0.7)
200 iterations Plot
bin200 = mybin(iter = 200, n = 10, p = 0.7)
500 iterations Plot
bin500 = mybin(iter = 500, n = 10, p = 0.7)
1000 iterations Plot
bin1000 = mybin(iter = 1000, n = 10, p = 0.7)
10000 iterations Plot
bin10000 = mybin(iter = 10000, n = 10, p = 0.7)
10000 iteration table
names(bin10000) = 0:10
bin10000## 0 1 2 3 4 5 6 7 8 9 10
## 0.0000 0.0000 0.0014 0.0104 0.0379 0.1103 0.1999 0.2654 0.2265 0.1187 0.0295Verify Values
dbin.tab = round(dbinom(0:10, size = 10, prob = 0.7), 4)
names(dbin.tab) = 0:10
dbin.tab## 0 1 2 3 4 5 6 7 8 9 10
## 0.0000 0.0001 0.0014 0.0090 0.0368 0.1029 0.2001 0.2668 0.2335 0.1211 0.0282Task 3
Sample without Replacement
marbles = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0)
sample(marbles, size = 5, replace = FALSE, prob = NULL)## [1] 1 0 1 1 0Sample with Replacement
sample(marbles, size = 5, replace = TRUE, prob = NULL)## [1] 1 0 0 1 1myhyper function
myhyper=function(iter=100,N=20,r=12,n=5){
# make a matrix to hold the samples initially filled with NA's
sam.mat=matrix(NA,nr=n,nc=iter, byrow=TRUE)
#Make a vector to hold the number of successes over the trials
succ=c()
for( i in 1:iter){
#Fill each column with a new sample
sam.mat[,i]=sample(rep(c(1,0),c(r,N-r)),n,replace=FALSE)
#Calculate a statistic from the sample (this case it is the sum)
succ[i]=sum(sam.mat[,i])
}
#Make a table of successes
succ.tab=table(factor(succ,levels=0:n))
#Make a barplot of the proportions
barplot(succ.tab/(iter), col=rainbow(n+1), main="HYPERGEOMETRIC simulation", xlab="Number of successes")
succ.tab/iter
}100 iterations Plot
hyper100 = myhyper(iter=100, n=5, N=20, r=12)
200 iterations Plot
hyper200 = myhyper(iter=200,n=5, N=20,r=12)
500 iterations Plot
hyper500 = myhyper(iter=500,n=5, N=20,r=12)
1000 iterations Plot
hyper1000 = myhyper(iter=1000,n=5, N=20,r=12)
10000 iterations Plot
hyper10000 = myhyper(iter=10000,n=5, N=20,r=12)
10000 iteration table
names(hyper10000) = 0:5
hyper10000## 0 1 2 3 4 5
## 0.0041 0.0508 0.2366 0.4018 0.2562 0.0505Verify Values
dhype = round(dhyper(x=0:5, m=12, n=8, k=5), 4)
names(dhype) = 0:5
dhype## 0 1 2 3 4 5
## 0.0036 0.0542 0.2384 0.3973 0.2554 0.0511Task 4
What does mysample() do?
mysample=function(n, iter=10,time=0.5){
for( i in 1:iter){
#make a sample
s=sample(1:10,n,replace=TRUE)
# turn the sample into a factor
sf=factor(s,levels=1:10)
#make a barplot
barplot(table(sf)/n,beside=TRUE,col=rainbow(10),
main=paste("Example sample()", " iteration ", i, " n= ", n,sep="") ,
ylim=c(0,0.2)
)
#release the table
Sys.sleep(time)
}
}The mysample function takes a vector n, number of iterations iter, and amount of time time. Basically it will sample 10 random samples from the vector, turn that sample to a factor, and then make barplot of that factor. Then the function will wait time time seconds and then loop iter-1 more times after the inital iteration.
Run Line
# Original Line
# mysample(n=1000, iter=30, time=1)
# Changed Line
mysample(n=1000, iter=1, time=0)
The line takes 30 seconds to run because it waits 1 second after each iteration, in this case 30 (30*1 = 30 seconds). But it also samples 10 random samples from the 1000 sided population vector.
Task 5
R Calculations
Calculation 1
choose(8,4)## [1] 70Calculation 2
1-ppois(4, lambda = 2)## [1] 0.05265302More R Calculations
More Calculations 1
# dnbinom(x=10-3,size=3,prob=0.4)
mynbin=function(y,r,p){
choose(y-1,r-1)*p^r*(1-p)^(y-r)
}
mynbin(10,3,0.4)## [1] 0.06449725More Calculations 2
pbinom(8, 15, 0.4)## [1] 0.9049526Task 6
Load Custom Package
bin = BestRPackage::abin(100, 10, 0.5)
bin##
## 0 1 2 3 4 5 6 7 8 9 10
## 0.00 0.00 0.07 0.20 0.23 0.17 0.14 0.16 0.03 0.00 0.00Task 7
negBinomialDistribution=function(iter=100,n=10, p=0.5){
# make a matrix to hold the samples initially filled with NA's
sam.mat=matrix(NA,nrow=n,ncol=iter, byrow=TRUE)
#Make a vector to hold the number of successes in each trial
succ=c()
for(i in 1:iter){
#Fill each column with a new sample
sam.mat[,i]=sample(c(1,0),n,replace=TRUE, prob=c(p,1-p))
#Calculate a statistic from the sample (this case it is the sum)
succ[i]=sum(sam.mat[,i])
}
#Make a table of successes
fail.tab=table(factor(n-succ,levels=0:n))
#Make a barplot of the proportions
iter.lab = paste0("iter = ", iter)
n.lab = paste0("n = ",n)
p.lab = paste0("p = ",p)
lab = paste0(iter.lab, n.lab, p.lab, sep=", ")
barplot(fail.tab/(iter), col=rainbow(n+1), main="Neg Binomial simulation", xlab="Number of successes")
fail.tab/iter
}
negBinomialDistribution(100, 10, 0.7)
##
## 0 1 2 3 4 5 6 7 8 9 10
## 0.01 0.10 0.29 0.24 0.22 0.12 0.02 0.00 0.00 0.00 0.00I think this is right, if not, at least I tried.